Question

A company has developed a new type of light bulb, and wants to estimate its mean lifetime. A simple random sample of 12 bulbs had a sample mean lifetime of 700 hours with a sample standard deviation of 71 hours. It is reasonable to believe that the population is approximately normal. Find the lower bound of the 95% confidence interval for the population mean lifetime of all bulbs manufactured by this new process.

Round to the nearest integer. Write only a number as your answer. Do not write any units.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 700

sample standard deviation = s = 71

sample size = n =12

Degrees of freedom = df = n - 1 = 12 - 1 = 11

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = 2.201

Margin of error = E = t/2,df * (s /n)

= 2.201 * (71 / 12)

Margin of error = E = 45

The lower bound of the 99% confidence interval estimate of the population mean is,

- E

700 - 45

655